This thesis investigates dominating sets in Kneser graphs as well as a selection of other topics related to graph domination. Dominating sets in Kneser graphs, especially those of minimum size, often correspond to interesting combinatorial incidence structures. We begin with background on the dominating set problem and a review of known bounds, focusing on algebraic bounds. We then consider this problem in the Kneser graphs, discussing basic results and previous work. We compute the domination number for a few of the Kneser graphs with the aid of some original results. We also investigate the connections between Kneser graph domination and the theory of combinatorial designs, and introduce a new type of design that generalizes the properties of dominating sets in Kneser graphs. We then consider dominating sets in the vector space analogue of Kneser graphs. We end by highlighting connections between the dominating set problem and other areas of combinatorics. Conjectures and open problems abound.

Saudi Arabia is one of the world’s largest exporters of oil and is known as the hub of Islam. It has been argued that the production of oil has a harmful effect on the economic and political status of women. Therefore, these tribal states are left with atypically strong patriarchal institutions where women are assigned to the domestic sphere. However, the international political pressure on Saudi Arabia to improve the position of women post the events of September the 11th 2001 has led the government to mobilise initiatives encouraging women into the public sphere. In addition, the depletion of oil resources has drawn the government’s attention to lessen its dependency on oil production and concentrate on private sector investment. Part of the government’s strategy has specifically focused on women, who hold much of the wealth in the country, to invest in the entrepreneurial sector in order to diversify the Saudi economy and provide employment to the rapidly increasing population. However, the laws continue to maintain women’s secondary position in society, as they are built on tribal customs and ideologies which treat women as ‘legal minors’ under the guardianship of her closest male relative. Furthermore, women are confined to jobs in the labour market which are deemed ‘suitable to their nature’, and thus, their entrepreneurial investment is constrained by gender-­‐discriminating laws and placed within certain industries. Research on Saudi women’s experiences of participating in the labour force are scarce, as is the literature on Saudi female entrepreneurs .This thesis adopts a relational multilevel framework with the lens of ‘patriarchal connectivity’ in investigating the salient micro-­‐ domestic, meso-­‐societal and macro-­‐ state opportunities and boundaries of 13 Saudi female entrepreneurs embedded in the patriarchal context. The research adopts a relational methodological approach, capitalising on qualitative in-­‐depth interviews with the female entrepreneurs to explore their entrepreneurial experiences, motivations, and the boundaries and opportunities they face. Furthermore, the study investigates women’s negotiation strategies in overcoming the patriarchal boundaries. The findings highlight the women’s ‘emancipatory’ motivations behind entrepreneurship. They also illustrate the nature of the ‘permeable boundaries’ within and across the patriarchal domestic, societal and state domains, which meant the women were paradoxically confronted by ‘enabling’ opportunities and ‘constraining’ boundaries in each of the domains. However, whilst the women did exercise agency at some permeable boundaries, this agency remained within the confines of a prevailing patriarchal structure.

For any graph parameter, the removal of a vertex from a graph can increase the parameter, decrease the parameter, or leave the parameter unchanged. This dissertation focuses on the case where the removal of a vertex decreases the parameter for the cases of independent domination and total domination. A graph is said to be independent domination vertex-critical, or i-critical, if the removal of any vertex decreases the independent domination number. Likewise, a graph is said to be total domination vertex-critical if the removal of any vertex decreases the total domination number. Following these notions, a graph is independent domination bicritical, or i-bicritical, if the removal of any two vertices decreases the independent domination number, and a graph is total domination bicritical if the removal of any two vertices decreases the total domination number. Additionally, a graph is called strong independent domination bicritical, or strong i-bicritical, if the removal of any two independent vertices decreases the independent domination number by two. Construction results for i-critical graphs, i-bicritical graphs, strong i-bicritical graphs, total domination critical graphs, and total domination bicritical graphs are studied. Many known constructions are extended to provide necessary and sufficient conditions to build critical and bicritical graphs. New constructions are also presented, with a concentration on i-critical graphs. One particular construction shows that for any graph G, there exists an i-critical, i-bicritical, and strong i-bicritical graph H such that G is an induced subgraph of H. Structural properties of i-critical graphs, i-bicritical graphs, total domination critical graphs, and total domination bicritical graphs are investigated, particularly for the connectedness and edge-connectedness of critical and bicritical graphs. The coalescence construction, which has appeared in earlier literature, constructs a graph with a cut-vertex and this construction is studied in great detail for i-critical graphs, i-bicritical graphs, total domination critical graphs, and total domination bicritical graphs. It is also shown that strong i-bicritical graphs are 2-connected and thus the coalescence construction is not useful in this case. Domination vertex-critical graphs (graphs where the removal of any vertex decreases the domination number) have been studied in the literature. A well-known result gives an upper bound on the diameter of such graphs. Here similar techniques are used to provide upper bounds on the diameter for i-critical graphs, strong i-bicritical graphs, and total domination critical graphs. The upper bound for the diameter of i-critical graphs trivially gives an upper bound for the diameter of i-bicritical graphs. For a graph G, the gamma-graph of G is the graph where the vertex set is the collection of minimum dominating sets of G. Adjacency between two minimum dominating sets in the gamma-graph occurs if from one minimum dominating set a vertex can be removed and replaced with a vertex to arrive at the other minimum dominating set. One can think of adjacency between minimum dominating sets in the gamma-graph as a swap of two vertices between minimum dominating sets. In the single vertex replacement adjacency model these two vertices can be any vertices in the minimum dominating sets, and in the slide adjacency model these two vertices must be adjacent in G. (Hence the gamma-graph obtained from the slide adjacency model is a subgraph of the gamma-graph obtained in the single vertex replacement adjacency model.) Results for both adjacency models are presented concerning the maximum degree, the diameter, and the order of the gamma-graph when G is a tree. / Graduate / 0405 / michaedwards@gmail.com

A broadcast is a function f that assigns an integer value to each vertex of a graph such that, for each v ∈ V , f (v) ≤ e (v), where e(v) is the eccentricity of v. The broadcast number of a graph is the minimum value of ∑ f(v) among all broadcasts f with the property that for each vertex u ∈ V, there exists some v ∈ V with f(v) > 0 such that d(υ,v) ≤ f(v). We present a new upper bound for the broadcast number of a graph in terms of its irredundance number and a new dual property of the broadcast number called the multipacking number of a graph. / Graduate

This work seeks to recover the critical spirit of conservatism and re-emphasize its goal of stability and resilience in society. I will argue that we should strive to view ourselves as deeply dependent and persistently vulnerable beings rather than free, equal, and rational individuals. An understanding of ourselves as embodied and interconnected patternings-in-the-world – res ecologia – will allow us to better recognize a diffuse violence at work in the modern world. I consider the nature of causation and suggest that the internal stability of res ecologia, when disrupted, should be a primary concern when considering the nature of violence and domination. I then invite us to understand the violence and domination arising in modern liberal societies – protocolic modulations – as abstract standardization that ensures efficient synchronization between individuated or atomized actors. Further, I suggest that the rapid modulations of this kind of protocolic domination disrupt the structural causation within and between res ecologia. In chapter five, I begin to show how this kind of violence and domination is manifest in and through the tradition of liberalism by tracing out a shared, underlying dualistic logic that simultaneously individuates and totalizes. In chapter six, I turn to the role of reason in creating freedom and legitimizing violence. Reason is seen to be contributing to both freedom and domination depending upon whether or not it creates resilience within society that resists standardizations. In chapter seven, I argue that the only way to effectively counter the excessive violence within the dualistic logic of liberalism is to cultivate an ethic of mutual support and restraint that invests society with stability and resilience. Finally, I conclude by contending that a resilient society requires intermediate structures and civil enterprises to instill tradition and reciprocal responsibilities in interdependent familial, socio-economic, and religious life. / Graduate / 0615 / jared.giesbrecht@gmail.com

Throughout four centuries of Ottoman domination, Salonika Jews had managed to preserve their particular ethnic identity and to occupy an important position in the economic life of the city. In 1912 Salonika was annexed to the Greek nation-state, and only decades later various sources of the early 1930s were emphasising the economic and social degradation of the Jewish community. Existing bibliography has tended to underline almost exclusively the role of Greek politics and Greek society as the major explanatory factor of the community's decline. This thesis challenges this approach and argues that intra-communal politics within the inter-war years had a significant share of responsibility for the crisis which threatened Salonika Jews in the late 1920s and early 1930s. Indeed, Jewish political elites were deeply split over issues of fundamental importance for the community, resulting in political deadlock. Consequently, the community was caught up in fierce ideological debates and was deprived of a solid communal leadership able to steer them through unsettled waters. In order to account for this explanation, the thesis reassesses as a first step Greek majority policies and argues that notwithstanding the numerous constraints which they imposed on the status of the Jews, the latter were left significant room in which to influence their own affairs. Secondly, this thesis explores the ways in which communal political leaders responded to and made use of their 'power'. By analysing the four major Jewish political parties in the inter-war years - the Zionists, the Assimilationists- Moderates, the Radicals (Mizrahi-Revisionists) and the Communists - on the basis of party competition and party ideologies which set 'Jewishness' at the centre of political discourse, it is shown that their constant ideological struggles over this issue rendered them unable to build up constructive political coalitions and find answers to the pressing economic and social needs faced by the community.

Thesis (M.A.)--Cleveland State University, 2008. / Abstract. Title from PDF t.p. (viewed on Apr. 14, 2009). Includes bibliographical references (p. 56-63). Available online via the OhioLINK ETD Center. Also available in print.

L'objectif de cette thèse est d'étudier sur le long terme, depuis la fin de l'époque achéménide jusqu'à celle du Haut-Empire (aux alentours de 235 après J.-C.) l'implantation de troupes et de vétérans perses, gréco-macédoniens, thraces, lyciens et romains, puis de leurs descendants, dans l'espace phrygien, région quelque peu marginale située dans le centre-ouest de l'Anatolie. Après avoir dans la première partie identifié et justifié stratégiquement les différents lieux d'installation, elle examine l'impact économique de celle-ci au travers de l'étude de la mainmise sur la terre et ses productions, du rôle des soldats en tant que producteurs et consommateurs et de leur implication dans la sécurisation du territoire. Sur un plan social, le quotidien des militaires, des vétérans et de leurs familles est ensuite examiné, de même que les formes prises par leur domination sur le reste de la population et leurs choix religieux. Le tout s'appuie sur un vaste corpus de plusieurs centaines d'inscriptions et de monnaies. / The objective of this thesis is to study on the long term, since the end of the achaemenid period until that of the roman Top-empire (near 235 AD) the setting-up of persian, greco-macedonian, thracian, lycian and roman troops and veterans, then of their descendants, in the Phrygian space, a little marginal region situated in west central Anatolia. Having in the first part identified and justified strategically the various places of installation, it examines the economic impact of this one through the study of the seizure by the earth and its productions, the role of the soldiers as producers and consumers and of their implication in the reassurance of the territory. On a social plan, the everyday life of the servicemen, the veterans and their families is then examined, as well as the forms taken by their domination on the rest of the population and their religious choices. The whole is based on a vast corpus of several hundred inscriptions and coins.

Dans cette thèse, nous travaillons sur les questions d'existence, puis d'absence de percolation de graphes orientés stationnaires dans l'espace euclidien. Les sommets de ces graphes sont distribués par un processus ponctuel de Poisson, et chaque sommet est connecté vers un unique autre sommet par une arête orientée. On parle alors de graphe orienté 'outdegree-one'. La règle permettant de construire l'ensemble des arêtes définie le graphe. Le premier résultat de la thèse fournit une condition suffisante pour qu'un graphe ne contienne pas de composantes connexes infinies. Un corollaire important de ce premier résultat affirme que le graphe orienté défini par une dynamique de segments grandissants décrites par D. Daley, G. Last et S. Ebert ne percole pas. Ce modèle défini à partir de segments poussant à vitesse constante dans le plan est un exemple de dynamique germes grains. Le second chapitre de la thèse propose une définition générale du modèle germes grains dans le plan et donne une condition suffisante pour qu'un modèle germes grains fixé puisse se caractériser par un graphe orienté "outdegree-one". Ce dernier résultat nous permet d'assurer l'existence de plusieurs graphe géométrique tout à fait naturel est riche en application. Le dernier résultat de la thèse consiste en l'absence de percolation d'une dynamique de segment grandissant qui généralise le modèle préalablement cité et dont l'existence découle de notre précédent résultat. / In this thesis, we investigate the existence and the absence of percolation for a large family of random graphs. We precisely study the oriented outdegree-one graphs based on a Poisson point process in $\mathbf{R}^{d}$. On the random pattern of points, each vertex is connected to its unique "neighbour" according to a fixed connection rule. This rule is translation-invariant and could also include a random part. Many natural simple dynamics can be described by an outdegree-one graph: the classical walk to the nearest neighbour on the graph defined by the hard sphere Lilypond model, etc.The first result of the thesis establishes sufficient conditions which guarantee the almost sure absence of infinite connected component in the graph. Precisely, each Poisson outdegree-one graph satisfying two precise assumptions does not percolate. The proof uses the mass transport principle, and an important result of stochastic domination. The most important corollary of this theorem is the absence of percolation of the line segment model with unit speed which has been conjectured in 2014 by D. Daley, S. Ebert and G. Last.The line segment model with random speed is well defined (as a stopped germs grains model) if the random velocity has an order $4$ moment. In the last chapter, we proved that the existence of an order $s$ exponential moment (with $s>1$) ensures the almost sure absence of percolation of the configuration of stopped segments. One of the key point of this result is the existence of a sufficiently small time $\mathbf{T}$ such that, before the time $\mathbf{T}$, any quick segments grows inside a boolean model which does not percolate. This argument should be used for different kinds of germs grains dynamics.

Given a graph with domination number γ, we find bounds on the maximum number of minimum dominating sets. First, for γ≥3, we obtain lower bounds on the number of γ-sets that do not dominate a graph on n vertices. Then, we show that γ-fold lexicographic product of the complete graph on n1/γ vertices has domination number γ and γn-O(nγ-γ/1) dominating sets of size γ. Finally, we see that a certain random graph has, with high probability, (i) domination number γ; and (ii) all but o(nγ) of its γ-sets being dominating.